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- W1574242095 abstract "We study the omega-limit sets $omega_X(x)$ in an isolating block $U$ of a singular-hyperbolic attractor for three-dimensional vector fields $X$. We prove that for every vector field $Y$ close to $X$ the set $ {xin U:omega_Y(x)$ contains a singularity$}$ is {em residual} in $U$. This is used to prove the persistence of singular-hyperbolic attractors with only one singularity as chain-transitive Lyapunov stable sets. These results generalize well known properties of the geometric Lorenz attractor [GW] and the example in [MPu]." @default.
- W1574242095 created "2016-06-24" @default.
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- W1574242095 date "2004-04-01" @default.
- W1574242095 modified "2023-09-26" @default.
- W1574242095 title "Omega-limit sets close to singular-hyperbolic attractors" @default.
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- W1574242095 doi "https://doi.org/10.1215/ijm/1258138404" @default.
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